1) The user gets to choose how to perform a particular activity.
2) Services can be found either automatically or by the user searching for services and saving them for later.
Don't the majority of users want this taken care of for them? Imagine going to facebook and having to find a service to perform a friend request. That's just an irritation for a benefit that most people don't want(wow I can send an invite using SMS with this service).
It's also notable that there's no styling on the examples. How is the UI going to be integrated, are all of the web intents supposed to follow a standard CSS format? How about the amount of space that service takes up on the page?
I suspect apis are popular because they're the best fit for sharing functionality on the web. Users want curated, integrated websites, not a set of mix 'n' match components.